1. 4.1 Powers of 10

2. QUESTION: What does it mean for 10 to be raised to zero or to a negative power?
STEP 1   Complete the table
Copy the table and complete the next two rows by evaluating 102 and 101.
Power
Standard form
103
1000
102
101
100
10–1
10–2
10–3

3. STEP 2   Find a pattern
Look at the rows you have completed. How does the standard form change each time the exponent decreases by 1?

4. STEP 3   Finish the table
Use the pattern you identified in Step 2 to complete the remaining rows in the table.

5. DRAW CONCLUSIONS: Use your observations to complete these exercises
104
109
10–4
10–6
Reasoning Let n be a positive integer. How many zeros are there in the standard form of 10n? in the standard form of 10–n?

6. Reverse Practice Write the number as a power of 10 1,000,000
1,000,000,000
.001
.0001

7. Negative Exponents to make fractions
A negative power of 10 can mean a number like .01, or you can use it to make a fraction
EXAMPLE: 10-2 means the decimal .01 and if we say the name it is one hundredth. So instead of making the decimal .01 we can make it
100
Try making 10-3 into a fraction WITHOUT turning it to a decimal first.

8. Extra Practice Write the negative power of 10 as a fraction 10-4 10-5
10-1
Order from least to greatest
14. 10, , 102, .001
, 102, 1, 10-3, 1 10